论文标题
硼摩尔序列Turán不平等的高级证据的简单证明
A simple proof of higher order Turán inequalities for Boros-Moll sequences
论文作者
论文摘要
最近，Guo获得了boros-Moll序列的高级Turán不平等现象$ \ {d_ \ ell（m）\} _ {\ ell = 0}^m $。在本文中，我们对此结果展示了另一种方法。我们的证明是基于Hou和Li得出的标准，该标准只需要检查与$ d_ \ ell（m）^2/（d _ {\ ell-1}（m）d _ {\ ell+ell+1}（m））$相关的四个与足够尖锐的界限相关的简单不平等。为此，我们采用了陈和GU在研究Boros-Moll多项式的反向超对数洞穴时的上限，并建立了$ d_ \ ell（m）^2/（d _ {\ ell-1}（\ ell-1}（m）d _ {m）d _ {\ ell+1}（m）$的$ cov的$ d _ \ ell（m）^2/（d _ {\ ell-1}（m）^2/（M） d_ \ ell（m）\} _ {\ ell = 0}^m $ for $ m \ geq 2 $。我们还显示了$ d_ \ ell（m）^2/（d _ {\ ell-1}（m）d _ {\ ell+1}（m））$的更清晰的下限，这可能可用于对Boros-Moll序列不平等的一些深度结果。
Recently, the higher order Turán inequalities for the Boros-Moll sequences $\{d_\ell(m)\}_{\ell=0}^m$ were obtained by Guo. In this paper, we show a different approach to this result. Our proof is based on a criterion derived by Hou and Li, which need only checking four simple inequalities related to sufficiently sharp bounds for $d_\ell(m)^2/(d_{\ell-1}(m)d_{\ell+1}(m))$. In order to do so, we adopt the upper bound given by Chen and Gu in studying the reverse ultra log-concavity of Boros-Moll polynomials, and establish a desired lower bound for $d_\ell(m)^2/(d_{\ell-1}(m)d_{\ell+1}(m))$ which also implies the log-concavity of $\{\ell! d_\ell(m)\}_{\ell=0}^m$ for $m\geq 2$. We also show a sharper lower bound for $d_\ell(m)^2/(d_{\ell-1}(m)d_{\ell+1}(m))$ which may be available for some deep results on inequalities of Boros-Moll sequences.
